Digital Communication, Prob of Error

[Third Person]

I'm reading the book by Sklar on Digital Communication.

I can't understand how the lower limit for the integral changes in the calculation of Bit Error Rate.

I have attached a figure, please have a look and tell me if you have an answer



I can't understand how the lower limit changes from (a1+a2)/2 to (a1-a2)/2sigma

Thanks

 

[Communications_Engineer]

it is simply a transformation from a typical gaussian distribution with mean µ=a2 and variance σ0 to normal distribution with µ=0, σ=1.

Replace u = (z-a2)/σ0

and change the lower limit of integration to (old limit - a2)/σ0